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General method of regularization. II: Relaxation proposed by suquet

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. We show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we prove an existence theorem for the limit analysis problem.

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

Mohammad Chowdhury, Kok-Keong Tan (2010)

Open Mathematics

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s...

Generalized communication conditions and the eigenvalue problem for a monotone and homogenous function

Rolando Cavazos-Cadena (2010)

Kybernetika

This work is concerned with the eigenvalue problem for a monotone and homogenous self-mapping f of a finite dimensional positive cone. Paralleling the classical analysis of the (linear) Perron–Frobenius theorem, a verifiable communication condition is formulated in terms of the successive compositions of f , and under such a condition it is shown that the upper eigenspaces of f are bounded in the projective sense, a property that yields the existence of a nonlinear eigenvalue as well as the projective...

Generalized degree in normed spaces.

Francisco Romero Ruiz del Portal (1992)

Publicacions Matemàtiques

We present a generalized degree theory for continuous maps f: (D, ∂D) → (E, E0), where E is a normed vectorial space, D is an open subset of Rk x E such that p1(D) is bounded in Rk and f is a compact perturbation of the second projection p2: Rk x E → E.

Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces

R. W. Hansell, L. Oncina (2005)

Czechoslovak Mathematical Journal

In this paper we deal with weakly upper semi-continuous set-valued maps, taking arbitrary non-empty values, from a non-metric domain to a Banach space. We obtain selectors having the point of continuity property relative to the norm topology for a large class of compact spaces as a domain. Exact conditions under which the selector is of the first Borel class are also investigated.

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